Question

Solve the radical. x+4=sqrt x+10 what is the extraneous solution to the radical equation

Answer 1

Answer:

-6 is an extraneous solution.

Step-by-step explanation:

We can start by solving this problem.

First, to remove the square root, we can square both sides.

$(x+4)^{2} = x + 10\\x^2 + 8x + 16 = x + 10$

Next, we can subtract both sides by (x+10)

$x^2 + 7x + 6 = 0$

Then, we can factor out the equation.

$(x+1)(x+6) = x^2 + 7x + 6 \\= 0$

Given this, it seems like -1 and -6 would be correct. Plugging this back into the original equation, though,

-1 + 4 = √(-1 + 10)

3 = 3

-6 + 4 = √(-6+10)

-2 ≠ 2

Therefore, -6 is an extraneous solution.